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## Theorem of Pythagoras

The theorem of Pythagoras for the relation between the length of the sides of a right triangle is well known by any high school student. Although the theorem is simple it is one of the very important theorems in mathematics, because the definition of distance in an Euclidean space is based upon this theorem. Any one using this theorem should therefore once have seen a proof. There are numerous proofs, but one very nice geometrical proof is shown here.

Theorem of Pythagoras
Given a right-angled triangle with sides a,b,c and c the hypotenuse (the side opposite the right angle) then $c^2 = a^2 + b^2$
Proof